$\dfrac{ 8l - 3m }{ 9 } = \dfrac{ -5l + 3n }{ -7 }$ Solve for $l$.
Solution: Multiply both sides by the left denominator. $\dfrac{ 8l - 3m }{ {9} } = \dfrac{ -5l + 3n }{ -7 }$ ${9} \cdot \dfrac{ 8l - 3m }{ {9} } = {9} \cdot \dfrac{ -5l + 3n }{ -7 }$ $8l - 3m = {9} \cdot \dfrac { -5l + 3n }{ -7 }$ Multiply both sides by the right denominator. $8l - 3m = 9 \cdot \dfrac{ -5l + 3n }{ -{7} }$ $-{7} \cdot \left( 8l - 3m \right) = -{7} \cdot 9 \cdot \dfrac{ -5l + 3n }{ -{7} }$ $-{7} \cdot \left( 8l - 3m \right) = 9 \cdot \left( -5l + 3n \right)$ Distribute both sides $-{7} \cdot \left( 8l - 3m \right) = {9} \cdot \left( -5l + 3n \right)$ $-{56}l + {21}m = -{45}l + {27}n$ Combine $l$ terms on the left. $-{56l} + 21m = -{45l} + 27n$ $-{11l} + 21m = 27n$ Move the $m$ term to the right. $-11l + {21m} = 27n$ $-11l = 27n - {21m}$ Isolate $l$ by dividing both sides by its coefficient. $-{11}l = 27n - 21m$ $l = \dfrac{ 27n - 21m }{ -{11} }$ Swap signs so the denominator isn't negative. $l = \dfrac{ -{27}n + {21}m }{ {11} }$